Final answer:
The rule that multiplying exponents with the same base results in the exponents being added together helps us understand why 6 raised to the power of 0 equals 1. By reversing the operation and continuously dividing by the base, we deduce that any number raised to the power of 0 must equal 1, which is the neutral element in multiplication.
Step-by-step explanation:
To understand why 60 = 1, we need to explore the rules of exponents. Consider the process of multiplying exponents with the same base, for example, 53 × 54 = 53+4 = 57. This example demonstrates that when we multiply two exponents with the same base, we simply add the exponents.
Now, if we apply this rule in reverse, decreasing the exponent should equate to dividing by the base. For instance, 53 ÷ 52 = 53-2 = 51. Following this pattern, 51 ÷ 51 would equal 50, because 1 minus 1 equals 0. Since 51 ÷ 51 is the same as dividing 5 by itself, which equals 1, this tells us that 50 must also equal 1.
This rule is general and applies to any base, including the number 6. When we talk about 60, we're essentially considering the result of dividing 6 by itself any number of times, always arriving at the value of 1. Moreover, in the realm of multiplication, 1 is the neutral element, akin to 0 in addition. Therefore, it is concluded that any number, including 6, raised to the power of 0 is 1, because we are left with the implicit 1 from no instances of the number being multiplied.